

These ncert book chapter wise questions and answers are very helpful for CBSE board exam. For each of the differential equations given below, indicate its order and degree if defined :. The highest order derivative present in this differential equation is and hence order of this differential equation if 2. The given differential equation is a polynomial equation in derivatives and highest power of the highest order derivative is 1.
The highest order derivative present in this differential equation is and hence order of this differential equation if 1. The given differential equation is a polynomial equation in derivatives and highest power of the highest order derivative is 3. The highest order derivative present in this differential equation is and hence order of this differential equation if 4. The given differential equation is not a polynomial equation in derivatives therefore, degree of this differential equation is not defined.
To verify: Function i is a solution of D. Differentiating both sides of eq. Again differentiating both sides w. Putting from eq. To verify: Function given by i is a solution of D. From i ,. To verify: Function given by eq. From eq. Equation of the given family of curves is.
Here number of arbitrary constants is one only. So, we will differentiate both sides of equation only once, w. Dividing eq. Given: Differential equation ���. Here each coefficient of and is of same degree, i. Putting these values in eq.
Now forming partial fraction of. Putting this value in eq. Squaring both sides and cross-multiplying,. We know that the circle in the first quadrant which touches the co-ordinates axes has centre where is the radius of the circle. Equation of the circle is. Differentiating with respect to.
Substituting value of in eq. Given: Differential Equation. Integrating both sides. Given: Differential equation. Integrating both sides, ���. Now [Completing the squares]. Multiplying every term in the numerator and denominator of L. Integrating both sides,. Now, curve i passes through. Therefore, putting in eq. Putting in eq. Dividing every term by we have. Now to evaluate , putting. Now putting in eq. It is not a homogeneous differential equation because of presence of only as a factor, yet it can be solved by putting i.
Putting ,. The general solution is I. This solution may be written as. Let P be the population of the village at time. According to the question, Rate of increase of population of the village is proportional to the number of inhabitants. Let us take the base year as. Putting value of in eq. To find the population in the year ,.
The general solution of the differential equation is:. We know that general solution of differential equation of the type is. Solution is. Ncert solution class 12 Maths includes text book solutions from both part 1 and part 2. Save my name, email, and website in this browser for the next time I comment.
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